Finite Group Databasebeta

← #10720211

Subgroups — #10720211

Order 768.

2278 conjugacy classes of subgroups.

The subgroup lattice has 1194 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#4989C211yesmaximal, characteristic, complemented
2C2×#4940C211yesmaximal, characteristic, complemented
3C2×C4×(C2×D3)⋊C4C211yesmaximal, characteristic, complemented
4C2×#4665C211yesmaximal, characteristic
5C2×#4665C211yesmaximal, characteristic
6C2×#4665C211yesmaximal, characteristic
7C2×D3×#95C211yesmaximal, characteristic, complemented
8C3×#1436C211yesmaximal, characteristic, complemented
9#71570C211yesmaximal, characteristic, complemented
10#69429C211yesmaximal, characteristic, complemented
11(C2×D3)⋊#95C211yesmaximal, characteristic, complemented
12#69417C211yesmaximal, characteristic, complemented
13#69414C211yesmaximal, characteristic, complemented
14#69408C211yesmaximal, characteristic, complemented
15#69401C211yesmaximal, characteristic, complemented
16#14140—31nomaximal, Sylow
17C23×D12C2211yescharacteristic
18C23×C4×D3C2211yescharacteristic
19C23×C4×D3C2211yescharacteristic
20C23×C4×D3C2211yescharacteristic
21C22×C3×C4⋊C4C2211yescharacteristic
22C22×C3×C42C2211yescharacteristic
23C22×(C2×D3)⋊C4C2211yescharacteristic
24C22×(C2×D3)⋊C4C2211yescharacteristic
25C22×(C2×D3)⋊C4C2211yescharacteristic
26C22×(C2×D3)⋊C4C2211yescharacteristic
27C22×(C2×D3)⋊C4C2211yescharacteristic
28C22×(C2×D3)⋊C4C2211yescharacteristic
29C22×(C2×D3)⋊C4C2211yescharacteristic
30C22×(C2×D3)⋊C4C2211yescharacteristic
31C22×(C2×D3)⋊C4C2211yescharacteristic
32C22×Dic3⋊C4C2211yescharacteristic
33C22×C4×Dic3C2211yescharacteristic
34C2×C3×#95C2211yescharacteristic
35C2×C3×#95C2211yescharacteristic
36C2×C3×#95C2211yescharacteristic
37C2×C3×#95C2211yescharacteristic
38C2×C3×#95C2211yescharacteristic
39C2×C3⋊#95C2211yescharacteristic
40C2×C3⋊#95C2211yescharacteristic
41C2×C3⋊#95C2211yescharacteristic
42C2×C3⋊#95C2211yescharacteristic
43C2×C3⋊#95C2211yescharacteristic
44C2×C3⋊#95C2211yescharacteristic
45C2×C3⋊#95C2211yescharacteristic
46C2×C3⋊#95C2211yescharacteristic
47C2×C3⋊#95C2211yescharacteristic
48C2×C3⋊#95C2211yescharacteristic
49C2×C3⋊#95C2211yescharacteristic
50C2×C3⋊#95C2211yescharacteristic
51C2×C3⋊#95C2211yescharacteristic
52#4989—24no—
53#4940—24no—
54C4×(C2×D3)⋊C4—24no—
55#4665—24no—
56#4665—24no—
57#4665C418yescomplemented
58D3×#95—24no—
59C2×#388—31no—
60C2×#386—31no—
61C2×#386—31no—
62C2×#386—31no—
63C2×#385—31no—
64C2×C4×C22⋊C4—31no—
65C22×#95—31no—
66#1443—31no—
67#1442—31no—
68#1440—31no—
69#1439—31no—
70#1437—31no—
71#1436D311yescharacteristic, complemented
72#1434—31no—
73C22⋊#95—31no—
74C24×D3C2311yescharacteristic
75C24×D3C2311yescharacteristic
76C23×C3×C4C2311yescharacteristic
77C23×C3×C4C2311yescharacteristic
78C23×C3×C4C2311yescharacteristic
79C23×C3×C4C2311yescharacteristic
80C23×C3×C4C2311yescharacteristic
81C23×C3×C4C2311yescharacteristic
82C23×C3×C4C2311yescharacteristic
83C23×Dic3C2311yescharacteristic
84C23×Dic3C2311yescharacteristic
85C23×Dic3C2311yescharacteristic
86C23×Dic3C2311yescharacteristic
87C23×Dic3C2311yescharacteristic
88C23×Dic3C2311yescharacteristic
89C22×D12—22no—
90C22×D12—22no—
91C22×D12—22no—
92C22×D12—22no—
93C22×D12—22no—
94C22×D12—22no—
95C22×D12C2×C414yes—
96C22×C4×D3—22no—
97C22×C4×D3—22no—
98C22×C4×D3—22no—
99C22×C4×D3—22no—
100C22×C4×D3—22no—
101C22×C4×D3—22no—
102C22×C4×D3—22no—
103C22×C4×D3—22no—
104C22×C4×D3—22no—
105C22×C4×D3—22no—
106C22×C4×D3—22no—
107C22×C4×D3—22no—
108C22×C4×D3—22no—
109C22×C4×D3—22no—
110C22×C4×D3—41no—
111C22×C4×D3—41no—
112C22×C4×D3—41no—
113C22×C4×D3—41no—
114C22×C4×D3—41no—
115C22×C4×D3—41no—
116C22×C4×D3C2×C414yes—
117C2×C3×C4⋊C4—22no—
118C2×C3×C4⋊C4—22no—
119C2×C3×C4⋊C4—41no—
120C2×C3×C42—22no—
121C2×C3×C42—22no—
122C2×C3×C42—41no—
123C2×(C2×D3)⋊C4—22no—
124C2×(C2×D3)⋊C4—22no—
125C2×(C2×D3)⋊C4—22no—
126C2×(C2×D3)⋊C4—22no—
127C2×(C2×D3)⋊C4—22no—
128C2×(C2×D3)⋊C4—22no—
129C2×(C2×D3)⋊C4—22no—
130C2×(C2×D3)⋊C4—22no—
131C2×(C2×D3)⋊C4—22no—
132C2×(C2×D3)⋊C4—22no—
133C2×(C2×D3)⋊C4—22no—
134C2×(C2×D3)⋊C4—22no—
135C2×(C2×D3)⋊C4—22no—
136C2×(C2×D3)⋊C4—22no—
137C2×(C2×D3)⋊C4—22no—
138C2×(C2×D3)⋊C4—22no—
139C2×(C2×D3)⋊C4—41no—
140C2×(C2×D3)⋊C4—41no—
141C2×(C2×D3)⋊C4—41no—
142C2×(C2×D3)⋊C4—41no—
143C2×(C2×D3)⋊C4—41no—
144C2×(C2×D3)⋊C4—41no—
145C2×(C2×D3)⋊C4C2×C414yes—
146C2×(C2×D3)⋊C4C2×C414yescomplemented
147C2×(C2×D3)⋊C4C2×C414yescomplemented
148C2×(C2×D3)⋊C4D414yes—
149C2×(C2×D3)⋊C4D414yes—
150C2×Dic3⋊C4—22no—
151C2×Dic3⋊C4—22no—
152C2×Dic3⋊C4—41no—
153C2×C4×Dic3—22no—
154C2×C4×Dic3—22no—
155C2×C4×Dic3—41no—
156C3×#95—22no—
157C3×#95—22no—
158C3×#95—22no—
159C3×#95—22no—
160C3×#95C2×C414yescomplemented
161C3⋊#95—22no—
162C3⋊#95—22no—
163C3⋊#95—22no—
164C3⋊#95—22no—
165C3⋊#95—22no—
166C3⋊#95—22no—
167C3⋊#95—22no—
168C3⋊#95—22no—
169C3⋊#95—22no—
170C3⋊#95—41no—
171C3⋊#95—41no—
172C3⋊#95C2×C414yescomplemented
173C3⋊#95D414yescomplemented
174C23×D4—31no—
175C24×C4—31no—
176C24×C4—31no—
177C24×C4—31no—
178C22×C4⋊C4—31no—
179C22×C4⋊C4C2×D311yescharacteristic
180C22×C22⋊C4—31no—
181C22×C22⋊C4—31no—
182C22×C22⋊C4—31no—
183C22×C22⋊C4—31no—
184C22×C22⋊C4—31no—
185C22×C22⋊C4—31no—
186C22×C22⋊C4—31no—
187C22×C22⋊C4—31no—
188C22×C22⋊C4—31no—
189C22×C42—31no—
190C22×C42C2×D311yescharacteristic
191#388—64no—
192#386—38no—
193#386—64no—
194#386—64no—
195#385—64no—
196C4×C22⋊C4—64no—
197C2×#95—31no—
198C2×#95—31no—
199C2×#95—31no—
200C2×#95—31no—
201C2×#95—31no—
202C2×#95—31no—
203C2×#95—31no—
204C2×#95—31no—
205C2×#95—31no—
206C2×#95—31no—
207C2×#95—31no—
208C2×#95—31no—
209C2×#95—31no—
210C2×#95—64no—
211C2×#95C2×D311yescharacteristic
212C2×#95C2×D311yescharacteristic
213C2×#95C2×D311yescharacteristic
214C2×#95C2×D311yescharacteristic
215C2×#95C2×D311yescharacteristic
216C24×C3C2411yescharacteristic
217C23×D3—21no—
218C23×D3—21no—
219C23×D3—21no—
220C23×D3—21no—
221C23×D3—21no—
222C23×D3—21no—
223C23×D3—21no—
224C23×D3—21no—
225C23×D3—21no—
226C23×D3—21no—
227C23×D3—21no—
228C23×D3—21no—
229C23×D3—21no—
230C23×D3—21no—
231C23×D3—21no—
232C23×D3—21no—
233C23×D3—21no—
234C23×D3—21no—
235C23×D3—21no—
236C23×D3—21no—
237C23×D3—21no—
238C23×D3—21no—
239C23×D3C22×C412yes—
240C23×D3C22×C412yes—
241C23×D3C2×D412yes—
242C23×D3C2×D412yes—
243C23×D3#4112yes—
244C23×D3#4112yes—
245C23×D3#4112yes—
246C23×D3#4112yes—
247C22×C3×C4—21no—
248C22×C3×C4—21no—
249C22×C3×C4—21no—
250C22×C3×C4—21no—
251C22×C3×C4—21no—
252C22×C3×C4—21no—
253C22×C3×C4—21no—
254C22×C3×C4—21no—
255C22×C3×C4—21no—
256C22×C3×C4—21no—
257C22×C3×C4—21no—
258C22×C3×C4—21no—
259C22×C3×C4—21no—
260C22×C3×C4—21no—
261C22×C3×C4—21no—
262C22×C3×C4—21no—
263C22×C3×C4—21no—
264C22×C3×C4—21no—
265C22×C3×C4—21no—
266C22×C3×C4—21no—
267C22×C3×C4—21no—
268C22×C3×C4—21no—
269C22×C3×C4—21no—
270C22×C3×C4—21no—
271C22×C3×C4—21no—
272C22×C3×C4—21no—
273C22×C3×C4—21no—
274C22×C3×C4—21no—
275C22×C3×C4—21no—
276C22×C3×C4—21no—
277C22×C3×C4—21no—
278C22×C3×C4—21no—
279C22×C3×C4—21no—
280C22×C3×C4—21no—
281C22×C3×C4—21no—
282C22×C3×C4—21no—
283C22×C3×C4—21no—
284C22×C3×C4—21no—
285C22×C3×C4—21no—
286C22×C3×C4—21no—
287C22×C3×C4C22×C412yes—
288C22×C3×C4C22×C412yes—
289C22×C3×C4C22×C412yes—
290C22×C3×C4C2×D412yes—
291C22×C3×C4C2×D412yes—
292C22×C3×C4C2×D412yes—
293C22×C3×C4#4112yes—
294C22×C3×C4#4112yes—
295C22×C3×C4#4112yes—
296C22×Dic3—21no—
297C22×Dic3—21no—
298C22×Dic3—21no—
299C22×Dic3—21no—
300C22×Dic3—21no—
301C22×Dic3—21no—
302C22×Dic3—21no—
303C22×Dic3—21no—
304C22×Dic3—21no—
305C22×Dic3—21no—
306C22×Dic3—21no—
307C22×Dic3—21no—
308C22×Dic3—21no—
309C22×Dic3—21no—
310C22×Dic3—21no—
311C22×Dic3—21no—
312C22×Dic3—21no—
313C22×Dic3—21no—
314C22×Dic3—21no—
315C22×Dic3—21no—
316C22×Dic3—21no—
317C22×Dic3—21no—
318C22×Dic3—21no—
319C22×Dic3—21no—
320C22×Dic3—21no—
321C22×Dic3—21no—
322C22×Dic3—21no—
323C22×Dic3—21no—
324C22×Dic3—21no—
325C22×Dic3—21no—
326C22×Dic3—21no—
327C22×Dic3—21no—
328C22×Dic3—21no—
329C22×Dic3—21no—
330C22×Dic3—21no—
331C22×Dic3—21no—
332C22×Dic3C22×C412yes—
333C22×Dic3C22×C412yes—
334C22×Dic3C2×D412yes—
335C22×Dic3C2×D412yes—
336C22×Dic3C2×D412yes—
337C22×Dic3C2×D412yes—
338C2×D12—28no—
339C2×D12—28no—
340C2×D12—28no—
341C2×D12—44no—
342C2×D12—44no—
343C2×D12—44no—
344C2×D12—44no—
345C2×C4×D3—28no—
346C2×C4×D3—28no—
347C2×C4×D3—28no—
348C2×C4×D3—28no—
349C2×C4×D3—44no—
350C2×C4×D3—44no—
351C2×C4×D3—44no—
352C2×C4×D3—44no—
353C2×C4×D3—44no—
354C2×C4×D3—44no—
355C2×C4×D3—44no—
356C2×C4×D3—44no—
357C2×C4×D3—44no—
358C2×C4×D3—44no—
359C2×C4×D3—44no—
360C2×C4×D3—44no—
361C2×C4×D3—44no—
362C2×C4×D3—44no—
363C2×C4×D3—44no—
364C2×C4×D3—44no—
365C2×C4×D3—44no—
366C3×C4⋊C4—44no—
367C3×C42—44no—
368(C2×D3)⋊C4—28no—
369(C2×D3)⋊C4—28no—
370(C2×D3)⋊C4—28no—
371(C2×D3)⋊C4—28no—
372(C2×D3)⋊C4—44no—
373(C2×D3)⋊C4—44no—
374(C2×D3)⋊C4—44no—
375(C2×D3)⋊C4—44no—
376(C2×D3)⋊C4—44no—
377Dic3⋊C4—44no—
378C4×Dic3—44no—
379C25—31no—
380C25—31no—
381C22×D4—34no—
382C22×D4—62no—
383C22×D4—62no—
384C22×D4—62no—
385C22×D4—62no—
386C22×D4—62no—
387C22×D4—62no—
388C23×C4—31no—
389C23×C4—31no—
390C23×C4—31no—
391C23×C4—31no—
392C23×C4—31no—
393C23×C4—31no—
394C23×C4—34no—
395C23×C4—62no—
396C23×C4—62no—
397C23×C4—62no—
398C23×C4—62no—
399C23×C4—62no—
400C23×C4—62no—
401C23×C4—62no—
402C23×C4—62no—
403C23×C4—62no—
404C23×C4—62no—
405C23×C4—62no—
406C23×C4—62no—
407C23×C4—62no—
408C23×C4—62no—
409C23×C4—121no—
410C23×C4—121no—
411C23×C4—121no—
412C23×C4—121no—
413C23×C4—121no—
414C23×C4—121no—
415C23×C4C22×D311yescharacteristic
416C23×C4C22×D311yescharacteristic
417C23×C4C22×D311yescharacteristic
418C23×C4C22×D311yescharacteristic
419C23×C4C22×D311yescharacteristic
420C23×C4C22×D311yescharacteristic
421C23×C4C22×D311yescharacteristic
422C2×C4⋊C4—22no—
423C2×C4⋊C4—22no—
424C2×C4⋊C4—41no—
425C2×C4⋊C4—62no—
426C2×C4⋊C4—62no—
427C2×C4⋊C4—121no—
428C2×C22⋊C4—34no—
429C2×C22⋊C4—34no—
430C2×C22⋊C4—34no—
431C2×C22⋊C4—34no—
432C2×C22⋊C4—34no—
433C2×C22⋊C4—62no—
434C2×C22⋊C4—62no—
435C2×C22⋊C4—62no—
436C2×C22⋊C4—62no—
437C2×C22⋊C4—62no—
438C2×C22⋊C4—62no—
439C2×C22⋊C4—62no—
440C2×C22⋊C4—62no—
441C2×C22⋊C4—62no—
442C2×C22⋊C4—62no—
443C2×C22⋊C4—62no—
444C2×C22⋊C4—62no—
445C2×C22⋊C4—62no—
446C2×C22⋊C4—62no—
447C2×C22⋊C4—62no—
448C2×C22⋊C4—62no—
449C2×C22⋊C4—121no—
450C2×C22⋊C4—121no—
451C2×C22⋊C4—121no—
452C2×C22⋊C4—121no—
453C2×C22⋊C4—121no—
454C2×C22⋊C4—121no—
455C2×C42—22no—
456C2×C42—22no—
457C2×C42—41no—
458C2×C42—62no—
459C2×C42—62no—
460C2×C42—121no—
461#95—22no—
462#95—22no—
463#95—22no—
464#95—22no—
465#95—34no—
466#95—34no—
467#95—62no—
468#95—62no—
469#95—62no—
470#95—62no—
471#95—62no—
472#95—62no—
473#95—62no—
474#95—62no—
475#95—62no—
476#95—121no—
477#95—121no—
478#95C4×D314yescomplemented
479C23×C3C23×C411yescharacteristic
480C23×C3C22×D411yescharacteristic
481C23×C3C22×D411yescharacteristic
482C23×C3C22×D411yescharacteristic
483C23×C3C2×#4111yescharacteristic
484C23×C3C2×#4111yescharacteristic
485C23×C3C2×#4111yescharacteristic
486C23×C3C2×#4111yescharacteristic
487C23×C3C2×#4111yescharacteristic
488C23×C3C2×#4111yescharacteristic
489C23×C3C2×#4111yescharacteristic
490C23×C3H(5,𝔽2)11yescharacteristic
491C23×C3H(5,𝔽2)11yescharacteristic
492C23×C3H(5,𝔽2)11yescharacteristic
493C23×C32−1+411yescharacteristic
494C22×D3—22no—
495C22×D3—22no—
496C22×D3—22no—
497C22×D3—22no—
498C22×D3—22no—
499C22×D3—22no—
500C22×D3—22no—
501C22×D3—22no—
502C22×D3—22no—
503C22×D3—22no—
504C22×D3—22no—
505C22×D3—22no—
506C22×D3—22no—
507C22×D3—22no—
508C22×D3—22no—
509C22×D3—22no—
510C22×D3—22no—
511C22×D3—22no—
512C22×D3—22no—
513C22×D3—22no—
514C22×D3—22no—
515C22×D3—22no—
516C22×D3—22no—
517C22×D3—22no—
518C22×D3—22no—
519C22×D3—22no—
520C22×D3—22no—
521C22×D3—22no—
522C22×D3—22no—
523C22×D3—22no—
524C22×D3—22no—
525C22×D3—22no—
526C22×D3—22no—
527C22×D3—22no—
528C22×D3—22no—
529C22×D3—41no—
530C22×D3—41no—
531C22×D3—41no—
532C22×D3—41no—
533C22×D3—41no—
534C22×D3—41no—
535C22×D3—41no—
536C22×D3—41no—
537C22×D3—41no—
538C22×D3—41no—
539C22×D3—41no—
540C22×D3—41no—
541C22×D3—41no—
542C22×D3—41no—
543C22×D3—41no—
544C22×D3—41no—
545C22×D3—41no—
546C22×D3—41no—
547C22×D3—41no—
548C22×D3—41no—
549C22×D3—41no—
550C22×D3—41no—
551C22×D3—41no—
552C22×D3—41no—
553C22×D3—41no—
554C22×D3—41no—
555C22×D3—41no—
556C22×D3—41no—
557C22×D3#11714yes—
558C22×D3C4×D414yes—
559C22×D3C4×D414yes—
560C22×D3#12114yes—
561C22×D3#12314yes—
562C22×D3#12414yes—
563C22×D3#12614yes—
564C2×C3×C4—22no—
565C2×C3×C4—22no—
566C2×C3×C4—22no—
567C2×C3×C4—22no—
568C2×C3×C4—22no—
569C2×C3×C4—22no—
570C2×C3×C4—22no—
571C2×C3×C4—22no—
572C2×C3×C4—22no—
573C2×C3×C4—22no—
574C2×C3×C4—22no—
575C2×C3×C4—22no—
576C2×C3×C4—22no—
577C2×C3×C4—22no—
578C2×C3×C4—22no—
579C2×C3×C4—22no—
580C2×C3×C4—22no—
581C2×C3×C4—22no—
582C2×C3×C4—22no—
583C2×C3×C4—22no—
584C2×C3×C4—22no—
585C2×C3×C4—22no—
586C2×C3×C4—22no—
587C2×C3×C4—22no—
588C2×C3×C4—41no—
589C2×C3×C4—41no—
590C2×C3×C4—41no—
591C2×C3×C4—41no—
592C2×C3×C4—41no—
593C2×C3×C4—41no—
594C2×C3×C4—41no—
595C2×C3×C4—41no—
596C2×C3×C4—41no—
597C2×C3×C4—41no—
598C2×C3×C4—41no—
599C2×C3×C4—41no—
600C2×C3×C4—41no—
601C2×C3×C4—41no—
602C2×C3×C4—41no—
603C2×C3×C4—41no—
604C2×C3×C4—41no—
605C2×C3×C4—41no—
606C2×C3×C4—41no—
607C2×C3×C4—41no—
608C2×C3×C4—41no—
609C2×C3×C4—41no—
610C2×C3×C4—41no—
611C2×C3×C4—41no—
612C2×C3×C4C4×D414yes—
613C2×Dic3—22no—
614C2×Dic3—22no—
615C2×Dic3—22no—
616C2×Dic3—22no—
617C2×Dic3—22no—
618C2×Dic3—22no—
619C2×Dic3—22no—
620C2×Dic3—22no—
621C2×Dic3—22no—
622C2×Dic3—22no—
623C2×Dic3—22no—
624C2×Dic3—22no—
625C2×Dic3—22no—
626C2×Dic3—22no—
627C2×Dic3—22no—
628C2×Dic3—22no—
629C2×Dic3—22no—
630C2×Dic3—22no—
631C2×Dic3—41no—
632C2×Dic3—41no—
633C2×Dic3—41no—
634C2×Dic3—41no—
635C2×Dic3—41no—
636C2×Dic3—41no—
637C2×Dic3—41no—
638C2×Dic3—41no—
639C2×Dic3—41no—
640C2×Dic3—41no—
641C2×Dic3—41no—
642C2×Dic3—41no—
643C2×Dic3—41no—
644C2×Dic3—41no—
645C2×Dic3—41no—
646C2×Dic3—41no—
647C2×Dic3—41no—
648C2×Dic3—41no—
649C2×Dic3—41no—
650C2×Dic3—41no—
651C2×Dic3—41no—
652C2×Dic3—41no—
653C2×Dic3—41no—
654C2×Dic3—41no—
655D12—416no—
656C4×D3—416no—
657C4×D3—416no—
658C4×D3—416no—
659C24—32no—
660C24—32no—
661C24—32no—
662C24—32no—
663C24—32no—
664C24—32no—
665C24—32no—
666C24—32no—
667C24—61no—
668C24—61no—
669C24—61no—
670C24—61no—
671C24—61no—
672C24—61no—
673C24—61no—
674C24—61no—
675C24—61no—
676C24—61no—
677C24—61no—
678C24—61no—
679C24—61no—
680C24—61no—
681C24—61no—
682C24—61no—
683C24—61no—
684C24—61no—
685C24—61no—
686C24—61no—
687C24—61no—
688C24—61no—
689C24C23×D311yescharacteristic
690C2×D4—68no—
691C2×D4—68no—
692C2×D4—68no—
693C2×D4—124no—
694C2×D4—124no—
695C2×D4—124no—
696C2×D4—124no—
697C22×C4—21no—
698C22×C4—21no—
699C22×C4—21no—
700C22×C4—21no—
701C22×C4—21no—
702C22×C4—21no—
703C22×C4—21no—
704C22×C4—21no—
705C22×C4—21no—
706C22×C4—21no—
707C22×C4—21no—
708C22×C4—21no—
709C22×C4—21no—
710C22×C4—21no—
711C22×C4—21no—
712C22×C4—21no—
713C22×C4—21no—
714C22×C4—21no—
715C22×C4—21no—
716C22×C4—21no—
717C22×C4—21no—
718C22×C4—21no—
719C22×C4—21no—
720C22×C4—21no—
721C22×C4—21no—
722C22×C4—21no—
723C22×C4—21no—
724C22×C4—21no—
725C22×C4—21no—
726C22×C4—21no—
727C22×C4—21no—
728C22×C4—21no—
729C22×C4—21no—
730C22×C4—21no—
731C22×C4—21no—
732C22×C4—21no—
733C22×C4—21no—
734C22×C4—21no—
735C22×C4—21no—
736C22×C4—21no—
737C22×C4—32no—
738C22×C4—32no—
739C22×C4—32no—
740C22×C4—32no—
741C22×C4—32no—
742C22×C4—32no—
743C22×C4—68no—
744C22×C4—68no—
745C22×C4—68no—
746C22×C4—61no—
747C22×C4—61no—
748C22×C4—61no—
749C22×C4—61no—
750C22×C4—61no—
751C22×C4—61no—
752C22×C4—61no—
753C22×C4—61no—
754C22×C4—61no—
755C22×C4—61no—
756C22×C4—61no—
757C22×C4—61no—
758C22×C4—61no—
759C22×C4—61no—
760C22×C4—61no—
761C22×C4—61no—
762C22×C4—61no—
763C22×C4—61no—
764C22×C4—61no—
765C22×C4—61no—
766C22×C4—61no—
767C22×C4—61no—
768C22×C4—61no—
769C22×C4—61no—
770C22×C4—61no—
771C22×C4—61no—
772C22×C4—61no—
773C22×C4—61no—
774C22×C4—61no—
775C22×C4—61no—
776C22×C4—61no—
777C22×C4—61no—
778C22×C4—61no—
779C22×C4—61no—
780C22×C4—61no—
781C22×C4—61no—
782C22×C4—68no—
783C22×C4—124no—
784C22×C4—124no—
785C22×C4—124no—
786C22×C4—124no—
787C22×C4—124no—
788C22×C4—124no—
789C22×C4—124no—
790C22×C4—124no—
791C22×C4—124no—
792C22×C4—124no—
793C22×C4—124no—
794C22×C4—124no—
795C22×C4—124no—
796C22×C4—124no—
797C22×C4—124no—
798C22×C4—124no—
799C22×C4—124no—
800C22×C4C2×C4×D312yes—
801C22×C4C2×C4×D312yes—
802C22×C4C2×C4×D312yes—
803C22×C4#23512yes—
804C22×C4#23512yes—
805C22×C4D3×D412yes—
806C22×C4D3×D412yes—
807C22×C4D3×D412yes—
808C22×C4#23912yes—
809C4⋊C4—44no—
810C4⋊C4—124no—
811C22⋊C4—68no—
812C22⋊C4—68no—
813C22⋊C4—68no—
814C22⋊C4—68no—
815C22⋊C4—124no—
816C22⋊C4—124no—
817C22⋊C4—124no—
818C22⋊C4—124no—
819C22⋊C4—124no—
820C42—44no—
821C42—124no—
822C22×C3C2×#11711yescharacteristic
823C22×C3C2×C4×D411yescharacteristic
824C22×C3C2×C4×D411yescharacteristic
825C22×C3C2×C4×D411yescharacteristic
826C22×C3C4×#4111yescharacteristic
827C22×C3#51811yescharacteristic
828C22×C3#52011yescharacteristic
829C22×C3C2×#12111yescharacteristic
830C22×C3C2×#12311yescharacteristic
831C22×C3#52511yescharacteristic
832C22×C3#52511yescharacteristic
833C22×C3C2×#12411yescharacteristic
834C22×C3C2×#12611yescharacteristic
835C22×C3#52911yescharacteristic
836C22×C3#52911yescharacteristic
837C22×C3#53811yescharacteristic
838C22×C3#53811yescharacteristic
839C22×C3#53911yescharacteristic
840C22×C3#53911yescharacteristic
841C22×C3D4211yescharacteristic
842C22×C3D4211yescharacteristic
843C22×C3#54611yescharacteristic
844C22×C3#54611yescharacteristic
845C22×C3#54611yescharacteristic
846C22×C3#54611yescharacteristic
847C22×C3#54611yescharacteristic
848C22×C3#54711yescharacteristic
849C22×C3#54711yescharacteristic
850C22×C3#54811yescharacteristic
851C22×C3#55111yescharacteristic
852C22×C3#55111yescharacteristic
853C22×C3#55211yescharacteristic
854C22×C3#55311yescharacteristic
855C22×C3#55311yescharacteristic
856C22×C3#55311yescharacteristic
857C2×D3—24no—
858C2×D3—24no—
859C2×D3—24no—
860C2×D3—24no—
861C2×D3—24no—
862C2×D3—24no—
863C2×D3—24no—
864C2×D3—24no—
865C2×D3—24no—
866C2×D3—24no—
867C2×D3—24no—
868C2×D3—24no—
869C2×D3—24no—
870C2×D3—24no—
871C2×D3—42no—
872C2×D3—42no—
873C2×D3—42no—
874C2×D3—42no—
875C2×D3—42no—
876C2×D3—42no—
877C2×D3—42no—
878C2×D3—81no—
879C2×D3—81no—
880C2×D3—81no—
881C2×D3—81no—
882C2×D3—81no—
883C2×D3—81no—
884C2×D3—81no—
885C2×D3—81no—
886C2×D3#38818yescomplemented
887C3×C4—24no—
888C3×C4—42no—
889C3×C4—42no—
890C3×C4—42no—
891C3×C4—42no—
892C3×C4—42no—
893C3×C4—42no—
894Dic3—42no—
895Dic3—42no—
896Dic3—42no—
897Dic3—42no—
898Dic3—42no—
899Dic3—42no—
900C23—34no—
901C23—34no—
902C23—34no—
903C23—34no—
904C23—34no—
905C23—34no—
906C23—34no—
907C23—62no—
908C23—62no—
909C23—62no—
910C23—62no—
911C23—62no—
912C23—62no—
913C23—62no—
914C23—62no—
915C23—62no—
916C23—62no—
917C23—62no—
918C23—62no—
919C23—62no—
920C23—62no—
921C23—62no—
922C23—62no—
923C23—62no—
924C23—62no—
925C23—62no—
926C23—62no—
927C23—62no—
928C23—62no—
929C23—62no—
930C23—62no—
931C23—62no—
932C23—62no—
933C23—62no—
934C23—62no—
935C23—62no—
936C23—62no—
937C23—62no—
938C23—62no—
939C23—62no—
940C23—62no—
941C23—62no—
942C23—121no—
943C23—121no—
944C23—121no—
945C23—121no—
946C23—121no—
947C23—121no—
948C23—121no—
949C23—121no—
950C23—121no—
951C23—121no—
952C23—121no—
953C23—121no—
954C23—121no—
955C23—121no—
956C23—121no—
957C23—121no—
958C23—121no—
959C23—121no—
960C23—121no—
961C23—121no—
962C23—121no—
963C23—121no—
964C23—121no—
965C23—121no—
966C23—121no—
967C23—121no—
968C23—121no—
969C23—121no—
970C23C22×C4×D311yescharacteristic
971C23C2×#23511yescharacteristic
972C23C2×#23511yescharacteristic
973C23C2×D3×D411yescharacteristic
974C23C2×D3×D411yescharacteristic
975C23C2×D3×D411yescharacteristic
976C23#100411yescharacteristic
977C23C2×#23911yescharacteristic
978C23#100711yescharacteristic
979C23D3×#4111yescharacteristic
980C23D3×#4111yescharacteristic
981C23D3×#4111yescharacteristic
982C23D3×#4111yescharacteristic
983C23#100911yescharacteristic
984C23#100911yescharacteristic
985D4—1216no—
986C2×C4—22no—
987C2×C4—22no—
988C2×C4—22no—
989C2×C4—22no—
990C2×C4—22no—
991C2×C4—22no—
992C2×C4—22no—
993C2×C4—22no—
994C2×C4—22no—
995C2×C4—22no—
996C2×C4—22no—
997C2×C4—22no—
998C2×C4—22no—
999C2×C4—22no—
1000C2×C4—22no—
1001C2×C4—22no—
1002C2×C4—22no—
1003C2×C4—22no—
1004C2×C4—22no—
1005C2×C4—22no—
1006C2×C4—22no—
1007C2×C4—22no—
1008C2×C4—22no—
1009C2×C4—22no—
1010C2×C4—41no—
1011C2×C4—41no—
1012C2×C4—41no—
1013C2×C4—41no—
1014C2×C4—41no—
1015C2×C4—41no—
1016C2×C4—41no—
1017C2×C4—41no—
1018C2×C4—41no—
1019C2×C4—41no—
1020C2×C4—41no—
1021C2×C4—41no—
1022C2×C4—41no—
1023C2×C4—41no—
1024C2×C4—41no—
1025C2×C4—41no—
1026C2×C4—41no—
1027C2×C4—41no—
1028C2×C4—41no—
1029C2×C4—41no—
1030C2×C4—41no—
1031C2×C4—41no—
1032C2×C4—41no—
1033C2×C4—41no—
1034C2×C4—62no—
1035C2×C4—62no—
1036C2×C4—62no—
1037C2×C4—62no—
1038C2×C4—62no—
1039C2×C4—62no—
1040C2×C4—62no—
1041C2×C4—62no—
1042C2×C4—62no—
1043C2×C4—62no—
1044C2×C4—62no—
1045C2×C4—62no—
1046C2×C4—62no—
1047C2×C4—62no—
1048C2×C4—62no—
1049C2×C4—62no—
1050C2×C4—62no—
1051C2×C4—62no—
1052C2×C4—1216no—
1053C2×C4—1216no—
1054C2×C4—1216no—
1055C2×C4—121no—
1056C2×C4—121no—
1057C2×C4—121no—
1058C2×C4—121no—
1059C2×C4—121no—
1060C2×C4—121no—
1061C2×C4—121no—
1062C2×C4—121no—
1063C2×C4—121no—
1064C2×C4—121no—
1065C2×C4—121no—
1066C2×C4—121no—
1067C2×C4—121no—
1068C2×C4—121no—
1069C2×C4—121no—
1070C2×C4—121no—
1071C2×C4—121no—
1072C2×C4—121no—
1073C2×C4—121no—
1074C2×C4—121no—
1075C2×C4—121no—
1076C2×C4—121no—
1077C2×C4—121no—
1078C2×C4—121no—
1079C2×C4#89314yes—
1080C2×C3C2×#38811yescharacteristic
1081C2×C3#229011yescharacteristic
1082C2×C3#231811yescharacteristic
1083C2×C3#235811yescharacteristic
1084C2×C3#235911yescharacteristic
1085C2×C3#236111yescharacteristic
1086C2×C3#236411yescharacteristic
1087C2×C3#242411yescharacteristic
1088C2×C3#242511yescharacteristic
1089C2×C3#244311yescharacteristic
1090C2×C3#244411yescharacteristic
1091C2×C3#247211yescharacteristic
1092C2×C3#248111yescharacteristic
1093C2×C3#248811yescharacteristic
1094C2×C3#251011yescharacteristic
1095D3—28no—
1096D3—82no—
1097C22—38no—
1098C22—64no—
1099C22—64no—
1100C22—64no—
1101C22—64no—
1102C22—64no—
1103C22—64no—
1104C22—64no—
1105C22—64no—
1106C22—64no—
1107C22—64no—
1108C22—64no—
1109C22—64no—
1110C22—64no—
1111C22—64no—
1112C22—122no—
1113C22—122no—
1114C22—122no—
1115C22—122no—
1116C22—122no—
1117C22—122no—
1118C22—122no—
1119C22—241no—
1120C22—241no—
1121C22—241no—
1122C22—241no—
1123C22—241no—
1124C22—241no—
1125C22—241no—
1126C22—241no—
1127C22C4×#23511yescharacteristic
1128C22#549011yescharacteristic
1129C22C2×#89311yescharacteristic
1130C22#550711yescharacteristic
1131C22D3×#11711yescharacteristic
1132C22#552711yescharacteristic
1133C22#553011yescharacteristic
1134C22C4×D3×D411yescharacteristic
1135C22C4×D3×D411yescharacteristic
1136C22#554511yescharacteristic
1137C22#554711yescharacteristic
1138C22#554711yescharacteristic
1139C22#555011yescharacteristic
1140C22#555011yescharacteristic
1141C22#555811yescharacteristic
1142C22#557411yescharacteristic
1143C22#558011yescharacteristic
1144C22#558011yescharacteristic
1145C22#558111yescharacteristic
1146C22#559011yescharacteristic
1147C22D3×#12111yescharacteristic
1148C22#560911yescharacteristic
1149C22#563011yescharacteristic
1150C22#563311yescharacteristic
1151C22#563711yescharacteristic
1152C22#563811yescharacteristic
1153C22D3×#12311yescharacteristic
1154C22#565411yescharacteristic
1155C22#565711yescharacteristic
1156C22D3×#12411yescharacteristic
1157C22#569211yescharacteristic
1158C22#569511yescharacteristic
1159C22D3×#12611yescharacteristic
1160C22#570411yescharacteristic
1161C22#572611yescharacteristic
1162C4—24no—
1163C4—42no—
1164C4—42no—
1165C4—42no—
1166C4—42no—
1167C4—42no—
1168C4—42no—
1169C4—122no—
1170C4—122no—
1171C4—122no—
1172C4—122no—
1173C4—122no—
1174C4—122no—
1175C3#1414011yescharacteristic, complemented, Sylow
1176C2—68no—
1177C2—242no—
1178C2#7357911yescharacteristic
1179C2#7375411yescharacteristic
1180C2#7377211yescharacteristic
1181C2#7459611yescharacteristic
1182C2#7460811yescharacteristic
1183C2#7489411yescharacteristic
1184C2#7494511yescharacteristic
1185C2#7501911yescharacteristic
1186C2#7532011yescharacteristic
1187C2#7534211yescharacteristic
1188C2#7552611yescharacteristic
1189C2D3×#38811yescharacteristic
1190C2#7620611yescharacteristic
1191C2#7621711yescharacteristic
1192C2#7662911yescharacteristic
subgroupG/H
center, FrattiniC24C23×D3
commutatorC23×C3C23×C4
FittingC3×#1436C2
socle, cosocleC24×C3C24
prime radicalC23×D12C22
hypercenter#1436D3
hypocenterC3#14140
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C24 ◁ #1436

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C2×#4989C2semidirect
2. C2×#4940C2semidirect
3. C2×C4×(C2×D3)⋊C4C2semidirect
7. C2×D3×#95C2semidirect
8. C3×#1436C2semidirect
9. #71570C2semidirect
10. #69429C2semidirect
11. (C2×D3)⋊#95C2semidirect
12. #69417C2semidirect
13. #69414C2semidirect
14. #69408C2semidirect
15. #69401C2semidirect
57. #4665C4semidirect
71. #1436D3semidirect
146. C2×(C2×D3)⋊C4C2×C4semidirect
147. C2×(C2×D3)⋊C4C2×C4semidirect
160. C3×#95C2×C4semidirect
172. C3⋊#95C2×C4semidirect
173. C3⋊#95D4semidirect
478. #95C4×D3semidirect
886. C2×D3#388semidirect
1175. C3#14140semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×#49892
C2×#49402
C2×C4×(C2×D3)⋊C42
C2×#46652
C2×D3×#952
C3×#14362
#715702
#694292
(C2×D3)⋊#952
#694172
#694142
#694082
#694012
#141403